# Two Higgs Doublet Models and $b\to s$ exclusive decays

## TL;DR

This paper calculates Wilson coefficients for exclusive $b o s\,\ell^+\ell^-$ decays within the Two Higgs Doublet Model, including $\,\mathcal{O}(m_b)$ corrections, and analyzes their phenomenological implications using recent experimental data.

## Contribution

It provides the first leading order Wilson coefficients for all $b\to s\ell^+\,\ell^-$ decays in 2HDM with detailed $\,\mathcal{O}(m_b)$ corrections and discusses their phenomenological impact.

## Key findings

- Constraints on 2HDM parameters from $B_s\to \mu^+\mu^-$ and $B\to K \mu^+\mu^-$ data.
- Impact of 2HDM on decay rates and observables.
- Discussion of decays involving $\,\tau$-leptons.

## Abstract

We computed the leading order Wilson coefficients relevant to all the exclusive $b\to s\ell^+\ell^-$ decays in the framework of Two Higgs Doublet Model (2HDM) with a softly broken $\mathbb{Z}_2$ symmetry by including the $\mathcal{O}(m_b)$ corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured $\mathcal{B}(B_s\to \mu^+\mu^-)$ and $\mathcal{B}(B\to K \mu^+\mu^-)_{\mathrm{high}-q^2}$, for which the hadronic uncertainties are well controlled, and discussed their impact on various types of 2HDM. A brief discussion of the decays with $\tau$-leptons in the final state is also made.